The Libyan suspect, in his 50s,was held at a location in south east England in what police described as “the first significant arrest” of the investigation into the 25-year-old officer’s killing in 1984.
Detectives have also arrested a man and a woman on suspicion of money laundering.
Commander Richard Walton, the head of the Met’s counter terrorism command, said the trio were arrested on Thursday morning.
The man arrested on suspicion of conspiracy to murder was also held on suspicion of money laundering.
The second man and the woman detained on suspicion of money laundering, who are aged in their 30s and 40s respectively, are also Libyans. They were arrested at separate addresses in London and south east England.
All three remain in custody and searches are under way across the country.
Mr Walton said: “Over the past 31 years we have never lost our resolve to solve this case, to bring to justice those who conspired to commit this act of murder.”
No one has ever been brought to justice for the murder of policewoman Yvonne Fletcher, who was shot dead outside Libya’s London embassy on April 17 1984. This is how events have unfolded since.
• April 17, 1984
Pc Yvonne Fletcher, 25, is shot by a sniper while policing a protest outside the Libyan embassy in St James’s Square, London, and 11 students are wounded.
She is pronounced dead shortly afterwards at Westminster Hospital. Her killer is thought to have been smuggled out of the country and back to Libya after the shooting. Her death leads to an 11-day siege of the building and the severing of diplomatic links between the UK and Libya.
The Libyan government accepts ‘’general responsibility’’ for the killing and agrees to pay compensation to Pc Fletcher’s family. British detectives also fly to Libya around that time to interview suspects but reportedly got little help.
Efforts to investigate the killing are stepped up when then prime minister Tony Blair meets Colonel Gaddafi after he agrees to dismantle his country’s weapons of mass destruction.
• April 2007
A report into Pc Fletcher’s death names the man who fired the fatal shot but concludes there is not enough evidence to bring a murder charge.
• June 2007
British detectives are able to interview the chief suspect for the first time following the normalisation of political ties with Libya. Detectives spend seven weeks in Libya interviewing witnesses and suspects.
• September 2009
It emerges that the Foreign Office has conceded that any trial for the shooting will take place in Tripoli. It is reported that the agreement was struck three years previously, when trade deals worth hundreds of millions of pounds were being negotiated. Campaigners for Pc Fletcher’s family brand the matter ‘’an absolute disgrace’’.
• February 2011
Major political protests begin in Libya against Gaddafi’s government and civil war breaks out.
• August 2011
The Libyan National Transitional Council (NTC) says that Abdulqadir al-Baghdadi, one of the suspects for Pc Fletcher’s murder, has been shot in the head. Junior diplomat Abdulmagid Salah Ameri, who was suspected of firing the fatal shots, is also thought to have died. The last named suspect in the killing believed to be still alive is Matouk Mohammed Matouk.
• October 20, 2011
Gaddafi dies after being captured by rebel troops, leading to scenes of wild jubilation in the country he formerly ruled as well as across the world. His death leads to new hope that Pc Fletcher’s killer will be brought to justice.
• November 2011
A senior British diplomat says he is confident that Scotland Yard detectives will soon be allowed to visit Libya.
• May 24, 2012
Prime Minister David Cameron announces that a Metropolitan Police team is to fly to Libya to continue the investigation after discussing the matter with the country’s interim prime minister Abdurrahim El-Keib during a visit to Downing Street. Mr El-Keib promises Libya will ‘’work very closely’’ with the UK.
• May 25, 2012
Mr El-Keib visits the spot where Pc Fletcher died and leaves a wreath of white roses and carnations.
• May 26, 2012
Mr El-Keib tells the Guardian Abdullah al-Senussi, one of Gaddafi’s most senior henchmen who is wanted by the International Criminal Court for crimes against humanity, is the ‘’black box’’ who knows who carried out the killing. ‘’I guarantee he was almost directly or indirectly involved in most if not all of the crimes (of the Gaddafi regime),” he tells the paper. “That doesn’t mean others weren’t involved. But he definitely knows who they were.’’
• June 14, 2012
Scotland Yard says two detectives from its counter-terrorism team have visited Tripoli where they met Libyan officials for “preliminary discussions” about how the investigation can be taken forward.
• July 17, 2012
Detectives from Scotland Yard’s counter-terrorism team pay a further visit to continue discussions with officials after authorities in the country asked them to return to Libya as soon as possible.
• April 17, 2014
A memorial service is held in St James’s Square to mark the 30th anniversary of Pc Fletcher’s murder. In a statement after the service, her family said: “We have had to move on with our lives but it is difficult to move forward when the past remains unresolved.”
• November 19, 2015
A Libyan man in his 50s is arrested in south-east England on suspicion of conspiring to murder Pc Fletcher, in what police describe as “the first significant arrest” of the investigation into her death.